In this paper we prove some symmetry results for en- tire solutions to the semilinear equation −∆ u =f (u) , with f non- increasing in a right neighbourhood of the origin. We consid er solutions decaying only in some directions and we give some s uffi- cient conditions for them to be radially symmetric with resp ect to those variables, such as periodicity or the pointwise decay of some derivatives
Symmetry properties of some solutions to some semilinear elliptic equations
MALCHIODI, ANDREA
;
2016
Abstract
In this paper we prove some symmetry results for en- tire solutions to the semilinear equation −∆ u =f (u) , with f non- increasing in a right neighbourhood of the origin. We consid er solutions decaying only in some directions and we give some s uffi- cient conditions for them to be radially symmetric with resp ect to those variables, such as periodicity or the pointwise decay of some derivativesFile in questo prodotto:
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